Question: Tiffany is 2 times as old as Vanessa. 24 years ago, Tiffany was 8 times as old as Vanessa. How old is Vanessa now?
Explanation: We can use the given information to write down two equations that describe the ages of Tiffany and Vanessa. Let Tiffany's current age be $t$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $t = 2v$ 24 years ago, Tiffany was $t - 24$ years old, and Vanessa was $v - 24$ years old. The information in the second sentence can be expressed in the following equation: $t - 24 = 8(v - 24)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $t$ and substitute it into our second equation. Our first equation is: $t = 2v$ . Substituting this into our second equation, we get: $2v$ $-$ $24 = 8(v - 24)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $2 v - 24 = 8 v - 192$ Solving for $v$ , we get: $6 v = 168.$ $v = 28$.